From Free Ride/The hub area, press Start
and then RB
twice to get to the Garage menu. The first option is Vehicle, choose that.
In this menu, you can see the various parts for your vehicle below. Two of them should have little grey hexagons next to them (should be engine and brake by default).
The brakes are much cheaper, so go to the breaks and upgrade all the slots for one of the parts such as Rainbow radius. The two upgrades for Rainbow radius should cost 200 and 400 motocoin.
Once the third part is unlocked, the achievement unlocks!